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3 questions
3
votes
1
answer
164
views
Mestre-type algorithm for higher-genus curves?
Is there an analogous algorithm for genus $g>2$ curves that, given a complete set of invariants, outputs a curve with those invariants?
(I'm interested in particular in $g=3$.)
Any references ...
- 61
2
votes
1
answer
162
views
DL-problem on abelian variety
Let $A$ be an abelian variety over $\mathbb{F_q}$ with dimension $n$. Let $q$ be a constant.
Is there polynomial algorithm of finding discrete logarithm in $A$?
UPD: really I don't undestend: can we ...
- 2,576
7
votes
1
answer
1k
views
Modular polynomials for elliptic curves point counting
The Schoof-Elkies-Atkin (SEA) algorithm (for counting points on elliptic curves over a finite field) performs computations over polynomials modulo some modular polynomials. Originally the "classical" ...
- 647